In this article, we propose a general group sequential framework for
clinical trials with a possibly censored, time-lagged outcome, which
leads to practical strategies for interim monitoring. Treatment
effect estimators are proposed via application of semiparametric
theory[1]}, [2]}, which dictates how censoring can
be taken into account and baseline and time-dependent covariate
information can be exploited in a principled way to increase precision
and thus yield stronger evidence for early stopping. Estimation of
the risk ratio via treatment-specific Kaplan-Meier estimators as
described above emerges as a simple special case, which can be
improved upon through incorporation of covariates. We show that the
test statistics based on these estimators have an independent
increments structure[3]}, which allows standard software
for constructing stopping boundaries[4]}, [5]}, [6]} to be used. Two
interim monitoring strategies are discussed: an information-based
monitoring approach under which the trial will continue, with possibly
a larger sample size than originally planned, until the full, target
statistical information accrues; and a fixed-sample size approach
appropriate in settings where the planned sample size cannot be increased
due to resource and other constraints. We focus on the common case of
two treatments; extension of the developments to more than two
treatments is possible[7]} and could be adapted to group
sequential methods for multi-arm trials[8]}, [9]}.
